The real field with convergent generalized power series

van den Dries, Lou; Speissegger, Patrick

doi:10.1090/S0002-9947-98-02105-9

The real field with convergent generalized power series
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by Lou van den Dries and Patrick Speissegger PDF

Trans. Amer. Math. Soc. 350 (1998), 4377-4421 Request permission

Abstract:

We construct a model complete and o-minimal expansion of the field of real numbers in which each real function given on $[0,1]$ by a series $\sum c_{n} x^{\alpha _{n}}$ with $0 \leq \alpha _{n} \rightarrow \infty$ and $\sum |c_{n}| r^{\alpha _{n}} < \infty$ for some $r>1$ is definable. This expansion is polynomially bounded.

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